Question

The ratio of areas within the electron orbits for the first excited state to the ground state for the hydrogen atom is

Answer 1

Radius of the nth orbit is given as
rn = (h2ϵ0/πme2) n2
For the ground state, n=1
For excited state, n=2
r2 = (h2ϵ0/πme2) n2
r1 = (h2ϵ0/πme2) n2
r2 / r1 = (h2ϵ0/πme2) n22 / (h2ϵ0/πme2) n12
r2 / r1 = n22 / n12
r2 / r1 = 22 / 12
r2 / r1 = 4 / 1
So the ratio between radii of the first orbital and the ground state radii is 4 / 1.